The 27-year-old scored for the fourth time in five days after his hat-trick against Reading to put his club level on points with leaders Cardiff and second-placed Middlesbrough and marginally behind on goal difference.
Ameobi struck in front of a crowd of 43,904 after just 15 minutes, although Newcastle were unable to find a second goal and it took good saves by Steve Harper from former Sunderland full-back Michael Gray and substitute Francis Jeffers to ensure all three points stayed on Tyneside.
Chris Hughton handed loan signing Danny Simpson a debut at right-back as Ryan Taylor moved into midfield to replace the injured Joey Barton.
It was they who took the lead with 15 minutes gone when Andy Carroll helped on Harper’s clearance and Ameobi controlled before half-volleying superbly inside keeper Lee Grant’s left post.
Grant did keep out Ameobi’s 28th-minute header from a Ryan Taylor corner, and although Owls striker Jermaine Johnson repeatedly caused problems for Fabricio Coloccini, the home side largely held sway before the break. Ryan Taylor almost wrapped up the win within seven minutes of the restart when he forced Grant into a fine save with a curling free-kick but in the end one was enough.
lIn League Two Chesterfield beat Notts County 2-1.
NEWCASTLE: Harper, Simpson, Steven Taylor, Coloccini, Jose Enrique, Ryan Taylor (Guthrie 89), Nolan, Smith, Gutierrez, Ameobi (Ranger 87), Carroll (Xisco 58).
SHEFFIELD WEDNESDAY: Grant, Buxton, Richard Wood, Purse, Spurr, Gray (Miller 73), Potter, O’Connor (Jeffers 80), McAllister (Esajas 73), Johnson, Tudgay.
Referee: Phil Dowd (Staffordshire).